Figures with the same shape, but not necessarily the same size,
are said to be “similar”.

(This definition allows for congruent figures to also be “similar”, where the ratio of the corresponding sides is 1:1.) 



Similar figures are figures that are the same shape, but not necessarily the same size.
Similar figures can also be defined in relation to transformations:

A similarity transformation is a transformation in which the image has the same shape as the preimage. The study of rigid transformations (isometries) showed a connection between congruent figures and the transformations of types called translations, reflections, and rotations. Rigid transformations preserve size and shape. 

Similarity transformations also include translations, reflections, and rotations, with the addition of dilations. Similarity transformations preserve shape, but not necessarily size, making the figures “similar”. Since it is possible for similar figures to have a scale factor of 1 (making the shapes the same size), it can be said that all congruent figures are also similar. Keep in mind, however, that most similar figures do not preserve size.
Are these triangles similar?
If it is possible to find one, or more, transformations that will move one triangle to coincide with the other, the triangles will be similar. 
Yes, these triangles are similar.
If ΔABC is dilated by a scale factor of 2, and then translated to the right and up, it will coincide with ΔDEF. 
We could have guessed that these triangles would be similar since they are both right triangles (their sides satisfy the Pythagorean Theorem), and their sides are generated from the same Pythagorean Triple of 3,4,5 (6,8,10 and 12,16,20). But, now we can “prove” that they are similar since we found the similarity transformations that allow one triangle to coincide with the other.
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